Consider Pimco Total Return, the giant bond mutual fund run by the renowned investor Bill Gross. In the year ended Sept. 30, its largest share class lost 0.74% — a respectable result, considering that the bond benchmark the fund seeks to beat, the Barclays U.S. Aggregate index, lost 1.89%.

But the fund’s investors, who yanked out $7.3 billion in May and June, right before it rebounded, did worse. Pimco Total Return’s largest share class had $169.3 billion in assets as of Sept. 30, 2012. If no one had put in or taken out a dime (other than to reinvest interest income and other payouts), these shares would have ended September 2013 with $168.1 billion, or 0.74% less. Instead, it finished at $157.1 billion—$11 billion less.

According to people familiar with the fund, its investors incurred an average loss of 1.4% over this period, nearly double the loss of the fund itself. That is because investors bought high and sold low, locking in the fund’s interim losses and missing its later gains. For the many people who believed they knew just when to buy and sell, that $11 billion is the collective toll of their imperfect self-knowledge.

What happened at Pimco Total Return, researchers have shown, isn’t the exception but the rule. Why do investors so often earn lower returns than their investments do? It is driven partly by arithmetic and partly by human nature.

A fund’s reported returns assume an investor bought at the beginning of a measurement period and held until the end, never adding or subtracting any money. That is the best way to measure the skill of the fund managers, who generally don’t control when investors give them cash or take it away.

But most investors don’t behave like statues. They buy and sell whenever they have or need the cash—or whenever the urge hits them.

If investors add money gradually when the portfolio is doing well, the fund’s reported returns will be higher than those of the people who own it—because not all of them were along for the whole ride.

Conversely, if investors add money gradually to a fund that is losing value, their average return will be better than that of the fund, since much of their money arrived too late to experience all the fund’s losses.

And investors don’t always add or withdraw money gradually. Often, they chase hot funds and flee cold ones. At 47 funds with assets of more than $1 billion, investors on average underperformed those funds by at least three percentage points over the 12 months ended Sept. 30, according to research firm Morningstar. Many of the funds were in formerly hot categories that suddenly went cold, like bonds and emerging markets.

Over the past five years, Morningstar recently found, investors trailed all their funds by an annual average of 1.17 percentage points. Other researchers have measured similar gaps between hedge funds and the supposedly ultrasophisticated investors who own them, as well as between stocks as a whole and the stockholding public.

Investors earn lower returns than their investments in exchange-traded funds, too—even though these funds are usually designed to match the returns of a market or sector. Preliminary research by finance professors Geoff Friesen of the University of Nebraska in Lincoln and Travis Sapp of Iowa State University suggests that at some ETFs, investors can underperform the fund by billions of dollars in just a few months.

The more narrowly focused a fund, and the more sharply it moves up and down relative to the market as a whole, the more likely investors– or their advisers — are to try chasing the ups and dodging the downs, says Fran Kinniry, an investment strategist at Vanguard Group.

With approximately 80% of fund assets now directed by financial advisers and other intermediaries, “it’s really the investment professionals themselves that are responsible for much of this behavior,” Mr. Kinniry says.

In research published in 2007, Messrs. Friesen and Sapp found that investors underperformed their U.S. stock funds by 1.6 percentage points annually between 1991 and 2004. At “load funds” sold by brokers, that gap averaged 1.9 percentage points per year; at no-load funds that investors bought directly, the difference was just 1.0 points.

“One would hope a financial adviser would be more cautious about trend-chasing,” Mr. Sapp says. “But we’re all people. What affects the individual investor to a large extent carries over to the financial adviser.”

Thus, instead of shooting themselves in the foot for free, nowadays most investors are “paying someone else to do it for them,” Mr. Friesen says.

So find a financial adviser who favors a handful of highly diversified funds rather than a jumble of narrowly focused, volatile funds. Make sure he tends to hold on for at least three years at a time. The simpler, smaller and smoother your collection of funds, the more likely you are to do as well as they do—instead of worse.